1 Objectives Define transformations and isometry Identify and draw translations Identify and draw reflections

2 Transformation definitions Transformation – a change in a geometric figure’s position, shape, or size Preimage – the original figure Image – the resulting figure after a transformation

3 Isometry defined Transformation in which the preimage and image have the same shape and size; also known as a rigid transformation

4 What is a translation? a transformation where all the points of a figure are moved the same distance in the same direction (a slide)

5 Transformation example Preimage (x,y) Image (x+3, y–2) U(1, 5)(4, 3) V(4, 1)(7, -1) W(5, 3)(8, 1) U′U′ W′W′ V′V′ (x,y)  (x+3, y–2) is the transformation rule or function (3, -2) is the translation vector

6 What is a reflection? a transformation that moves a figure by flipping it across a line.

7 Reflections – Line of symmetry The line of reflection is the perpendicular bisector of every segment connecting a point and its image; So if you connect one vertex to its image, the midpoint lies on the line of symmetry

8 Reflection across the x-axis Reflect the figure with the given vertices across the x axis. The reflection of (x, y) is (x,–y). X(2,–1) X’(2, 1) Y(–4,–3) Y’(–4, 3) Z(3, 2) Z’(3, –2) Y X Z X’ Y’ Z’